1. What is Impulse Response?

The impulse response h(t) of a linear time-invariant (LTI) system characterizes the system's output when presented with a brief input signal (impulse). It completely describes the behavior of any LTI system.

2. How Does the Calculator Work?

The calculator uses the impulse response formula:

Where:

• \( h(t) \) — Impulse response of the system
• \( y(t) \) — Output signal from the system
• \( x(t) \) — Input signal to the system

Explanation: For LTI systems, the ratio of output to input signals gives the impulse response, which can be used to predict system behavior for any input.

3. Importance of Impulse Response

Details: The impulse response is fundamental in signal processing and control theory. It allows complete system characterization, convolution operations, and frequency response analysis through Fourier transformation.

4. Using the Calculator

Tips: Enter the measured output signal and known input signal values. Both values must be positive numbers. The calculator will compute their ratio to determine the impulse response.

5. Frequently Asked Questions (FAQ)

Q1: What is an LTI system?
A: Linear Time-Invariant systems satisfy superposition principle (linearity) and have parameters that don't change with time (time-invariance).

Q2: Why is impulse response important?
A: It completely characterizes an LTI system - knowing h(t) allows prediction of system response to any arbitrary input through convolution.

Q3: What's the difference between impulse response and transfer function?
A: The transfer function is the Laplace transform of the impulse response. Both fully describe the system but in different domains.

Q4: Can this be used for discrete-time systems?
A: Yes, the discrete-time version uses the same principle with h[n] = y[n]/x[n] for LTI systems.

Q5: What if my system isn't LTI?
A: This simple ratio calculation only works for LTI systems. Nonlinear or time-varying systems require more complex analysis.